Equilateral Triangle Proof

Date: 11/05/2001 at 21:14:06
From: Chenelle Horton
Subject: Geometry
The question that I am trying to answer is as follows:
Let a, b, and c be the lengths of the sides of a triangle. Show that
if a*a + b*b + c*c = bc + ca + ab, then the triangle is equilateral.
I have drawn a picture, but I don't know how to show the equation is
true without numbers. Can you give me a hint as to how to start?
Thank you so much,
Chenelle